Question

A person can jump a horizontal distance of 1.57 m on the Earth. The acceleration of gravity is 8.21 m/s 2 . How far could he jump on the Moon, where the free-fall acceleration is 0.153g?

Answer 1

The person could jump about 6.43 times higher on the Moon than on Earth if the takeoff speed is the same in both locations.

Step-by-step explanation:

To find out how much farther a person could jump on the Moon compared to Earth, we need to use the concept of gravitational acceleration. The gravitational acceleration on the Moon is about 1/6 that of Earth. Since the takeoff speed of the astronaut is the same in both locations, we can use the equation: distance = (takeoff speed)^2 / (2 * gravitational acceleration).

Let's say the person can jump a distance of 1.57 m on Earth, with a gravitational acceleration of 8.21 m/s^2. On the Moon, the gravitational acceleration is 0.153 * 8.21 m/s^2. Plugging these values into the equation, the person could jump a distance of approximately 10.09 m on the Moon. This means the person could jump about 6.43 times higher on the Moon than on Earth.

Answer 2

Horizontal distance that a person can jump on the ground is known as horizontal range.

Horizontal range can be calculated by the formula of projectile motion which is given as

`R = (v^2sin2\theta)/(g)`

here for the maximum possible range of jump we can say that he must have to jump at 45 degree

so that the value of the range will be maximum in above equation

`R = (v^2)/(g)`

now if we compare the jump of a person on two planets then as per the capability of the person then velocity of jump will remain same on two planets so we can say

`(R_1)/(R_2) = (g_2)/(g_1)`

`(1.57)/(R_2) = (0.153g)/(g)`

here it is given that on Earth the acceleration is g = 8.21 m/s^2[/tex]

and on moon it is g' = 0.153g

now we have

`(1.57)/(R_2) = \frac{0.153}`

`R_2 = (1.57)/(0.153)`

`R_2 = 10.3 m`

So the person can jump a distance of 10.3 m on the Moon